Question

.4 (a) Construct Laspeyres, Paasche and Fisher indices from the following data: Item 2018 2019 Price (Rs.) Expenditure (Rs.) Price (Rs.) Expenditure (Rs.) A 10 60 15 75 B 12 120 15 150 C 18 90 27 81 D 8 40 12 48

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Answer 1

Given

Refer the attachment for the given data.

In all the following index

$p _{o} \: \: \: \: p_{1}$

stands for the Intial price , current price and

$q_{o } \: \: \: \: \: q_{1}$

stands for Intial quantity, current quantity.

Construction of Laspeyres index.

It is used in the statistics for calculating the price of goods consumed in the base period.

$l = \frac{ \sigma \: p_{1} \: q_{1} }{ \sigma \: p_{o} \: q_{o} } \times 100$

$l = \frac{(15 \times 6) + (15 \times 10) + (27 \times 5) + (5 \times 12)}{(10 \times 6) + (12 \times 10) + (18 \times 5)} \times 100$

$l = 140.32$

Construction of Paasche index.

It is used in the statistics for calculating the price of goods consumed in current period.

$l = \frac{ \sigma \: p_{1} \: q_{1}}{ \sigma \: p_{o} \: \: q_{o} } \times 100$

$l = \frac{(15 \times 5) + (15 \times 10) + (27 \times 3) + (12 \times 4)}{(1 \times 5) + (12 \times 10) + (18 \times 3) + (8 \times 4)} \times 100|$

$l = 138.28$

Construction of Fisher index.

It is used in statistics for calculating development price for goods from base and current period.

$f = \sqrt{ \frac{ \sigma \: p_{1} q_{0} }{ \sigma \: p \: q_{o} } \times \frac{ \sigma \: p_{1} q_{1} }{ \sigma \: p_{o} \: q_{1} } \times 100}$

$f = \sqrt{l \times p}$

$f = \sqrt{140.322 \times 138.28}$

$f = 139.2972$